Calculate structure

An important part of protein structure is the secondary structure which is made up of helices, sheets and turns, and with limitations as described in How Jmol Determines Secondary Structure  Jmol is capable of determining and displaying these three types of structures. The calculate structure command which re-calculates the secondary structure does a more fundamental identification of these secondary structures but is not available in Jmol 11.8 which is used in Proteopedia as of June 2011 but is available in Jmol ver. 12. Calculate hbonds structure is also available in ver. 12, and it identifies and displays the hbonds involved in these three types of secondary structures. Any one page of Proteopedia can be run in the signed ver. 12 by appending "?JMOLJAR=http://chemapps.stolaf.edu/jmol/docs/examples-12/JmolAppletSigned0.jar" to the url of the page and reloading the page. The user must give permission for the signed version of Jmol to open, and when it does it has a red frank, whereas in the unsigned version it is grey. Click on the Jmol frank, in the main menu which opens click on Console, in the bottom box enter the commands: select protein; calculate structure; cartoon; color structure; calculate hbonds structure and then click Run. The objectives of this article is:
 * To describe briefly what structures are identified by calculate structure and how it is done.
 * To compare its results with other ways of identifying and classifying these structures.
 * To illustrate with two examples.



Basis of Secondary Structure Determination
Calculate structure is based on Defined Secondary Structure of Protein (DSSP), a program written in Pascal. The secondary structure recognition algorithms used in DSSP are based mainly on hydrogen-bonding patterns along with geometric structures, such as bends. There are two different hydrogen-bonding patterns which are recognized. The one determines the value of n in the expression i + n (i is a residue that forms a hydrogen bond with a residue n residues removed from residue i.) where n = 3, 4 or 5. These values define three types of turns. A peptide segment that has repeating turns of the same type are called 310-helix, α-helix, or п-helix, respectively. If the turn is isolate, it is simply called an n-turn. The other recognized pattern is a hydrogen bond which is between residues which are not close together in sequence. This type of hydrogen bond is called a bridge. Kabsch & Sanders define a ladder as a "set of one or more consecutive bridges of identical type" and a sheet as a "set of one or more ladders connected by shared residues". Bends are peptide segments with high curvature, and the determination of curvature involves angles of the Cα. Bends can overlap with helices and turns. After its completion the results of calculate structure computation are printed in the upper box of the console. One part of that output is a summary of the different types of secondary structure with each type having a one letter identifier. It is possible for a residue or a segment of residues to be assigned more than one structural type, and for this reason the key of structural types given below is rank ordered in decreasing priority of assignment. With bend having the lowest priority in assignment a structure is identified as a bend only if it is not assigned any other structural type. The summary for myohemerytherin (2mhr) is given below.

Other Definitions of Turns
The DSSP determination of helices and β-sheets is in agreement with the generally accepted view of these two structures, but the DSSP determination of turns is not as specific as the generally accepted definition of turns. As described above DSSP identifies turns that have 3, 4, or 5 residues with a backbone hbond being present between the first and the last residues. The presence of the hbond is a requirement to be classified as a turn. Phi and psi torsional angles of the Cα are not used by the DSSP procedure, but the generally accepted definitions of turns involve these angles.

All types of β-turns contain four residues and therefore would be included with the 4-turns found by DSSP. The classes of β-turns are defined by the range of psi and phi values for the second and third residues. There is often a hbond between residues one and four (i + 3) of β-turns, but there is not an absolute requirement for one. In three classes a Pro in the third position has the cis configuration which does not permit the formation of a hbond (View display of structure.). The turns in these three classes are not detected by DSSP since they do not contain a hbond.

All γ-turns contain three residues having a hbond between residues i and i + 1 and would be included with the 3-turns found by DSSP. The classic γ-turns have phi and psi values at residue i + 1 of +75.0 ± 40 and -64 ± 40, respectively, and the inverse γ-turns have phi and psi values at residue i + 1 of -79 ± 40 and +69 ± 40, respectively.

Illustrations


The user is urged to use the above directions to open Jmol version 12 and to run the calculate structure and the accompanying commands so that the resulting display can be compared with the summary below. (Restore initial scene ) Without displaying the images generated by calculate structure and calculate hbonds structure the activities and comparisons described below can not be performed. The α-helices and 310-helices displayed by calculate structure can easily be associated with the corresponding peptide segments in the summary, but the turns need some additional explanation. One might expect that the segments in the summary that have one residue, two residues, and three residues are the interior residues of 3-turns, 4-turn and 5-turns, respectively. This is often the case, but in many cases it is not this simple. The turn may overlap or partially overlap with a structure that has higher priority, so that a one residue segment in the summary could represent a 4-turn. Another possibility could be that one turn is nested in a second one. In order to clarify the specific nature of the turn one needs to determine between which two residues the hbond occurs and thereby which type of n-turn is present. Looking closely at a blue colored trace find the dashed line representing a hbond, and hovering over the trace where the dashed line meets the trace reveals the number of the residue that is hydrogen bonded. Go to the other end of the dashed line and determine the residue number at that end. The two numbers should be i and i + n. More detail on myohemerytherin's turns and their hbonds are given below with green links and description. Measuring the values of the torsional angles (Directions to display these angles) of the interior residues of the turn is another way of revealing the nature of the turns, because these values can be used to classify the turn as a β-turn or γ-turn. The description below identifies the β-turn class of each of the turns.

The second T in the myohemerytherin summary is identified as segment A:68_A:69. This turn serves to illustrate that most often 4-turns (β-turns) are identified in the summary by their two central residues. Most of the β-turns in myohemerythrin are exceptions to this generalization, but in glycogen phosphorylase (below) it does hold in the majority of cases. Since Proteopedia uses Jmol 11.8, calculate hbonds structure does not function in the green link, so in order to display the hbonds after clicking a green link the user must run the calculate hbonds structure command in the console. One can see that the hbond is between residues 67 and 70 making it a 4-turn, and the values for the phi and psi angles of residues 2 and 3 make it a class I β-turn. Notice, however, that part of residues 67 and 68 are colored white rather than blue. The first T is identified by a two residue segment, but the two residues, A:65_A:66, are the last two in the turn. Displaying the hbond shows that it is between residues A:63-A:66 which qualifies it for a 4-turn and the torsional angles classify it as type I β-turn. As shown by their coloration the first two residues also qualify as α-helix and are displayed as such since a helix has priority over a turn. The last T identifies a three residue segment indicating a 5-turn. Calculate hbonds structure shows hbonds between 114 and 117 (4-turn and type II β-turn) and between 114 and 118 (5-turn). A β-turn is nested in a 5-turn. Residue 114 is part of the 310-helix so it is not colored blue.

The two remaining T's have one residue segments, and these could possibly be a 3-turn, but displaying backbone with hbonds reveals that they are 4-turn with some of the other residues also being part of a helix which has priority over a turn. Both of these turns are class I β-turn.

There are two β-turns that are not detected by DSSP, and they are both class IVB which do not have a hbond. They are located at residues 5-8 and 88-91. Run calculate hbonds structure to confirm that there are no hbonds in these turns. SUMMARY for Myohemerytherin: G : A:12_A:14 H : A:19_A:37 H : A:41_A:64 T : A:65_A:66    Display turn T : A:68_A:69    Display turn ; run the command calculate hbonds structure in the console to see the hbonds H : A:70_A:85 T : A:86_A:86          Display turn H : A:93_A:109 T : A:110_A:110       Display turn G : A:111_A:114 T : A:115_A:117    Display turn Key - H: α-helix; B: β-bridge; E: β-strand; G: 310-helix; I: π-helix; T: 3-, 4-, 5-turn; S: bend.

Show structure of domain 2 of chain A glycogen phosphorylase SUMMARY for Domain 2 of Chain A Glycogen Phosphorylase: B : A:486_A:486 T : A:488_A:488 I : A:489_A:494 T : A:495_A:495 H : A:497_A:507 G : A:510_A:513 G : A:515_A:524 T : A:525_A:526 H : A:528_A:551 E : A:562_A:567 G : A:572_A:574 H : A:576_A:592 T : A:594_A:595 E : A:601_A:606 T : A:611_A:612 H : A:614_A:632 T : A:635_A:638 E : A:640_A:644 H : A:650_A:659 E : A:662_A:665 T : A:669_A:670 T : A:676_A:677 H : A:678_A:682 T : A:683_A:685 E : A:687_A:691 T : A:694_A:695 H : A:696_A:703 G : A:705_A:707 E : A:709_A:711 H : A:715_A:724 T : A:728_A:728 H : A:729_A:734 H : A:736_A:746 T : A:747_A:750 T : A:752_A:753 G : A:755_A:758 H : A:759_A:768 T : A:773_A:773 G : A:774_A:776 T : A:777_A:777 H : A:778_A:791 H : A:794_A:806 T : A:807_A:807 G : A:808_A:811 B : A:812_A:812 H : A:813_A:821 T : A:822_A:825

